Related papers: Volume extrapolation via eigenvector continuation
Enlightened from the inverse consideration of the stable continuous-time dynamics evolution, the Variation Evolving Method (VEM) analogizes the optimal solution to the equilibrium point of an infinite-dimensional dynamic system and solves…
This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out…
The enriched effect calculus (EEC) is an extension of Moggi's computational metalanguage with a selection of primitives from linear logic. This paper explores the enriched effect calculus as a target language for continuation-passing-style…
Variational Autoencoders (VAEs) are powerful generative models widely used for learning interpretable latent spaces, quantifying uncertainty, and compressing data for downstream generative tasks. VAEs typically rely on diagonal Gaussian…
We introduce (U)NFV, a modular neural network architecture that generalizes classical finite volume (FV) methods for solving hyperbolic conservation laws. Hyperbolic partial differential equations (PDEs) are challenging to solve,…
The variational quantum eigensolver (VQE) has emerged as one of the leading quantum algorithms for solving electronic structure problems on near-term noisy intermediate-scale quantum devices. However, its practical application to quantum…
We introduce the Cyclic Variational Quantum Eigensolver (CVQE), a hardware-efficient framework for accurate ground-state quantum simulation on noisy intermediate-scale quantum (NISQ) devices. CVQE departs from conventional VQE by…
Deep Learning models encode rich semantic information in their hidden representations. However, it remains challenging to understand which parts of this information models actually rely on when making predictions. A promising line of…
In a number of problems in computational physics, a finite sum of kernel functions centered at $N$ particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries. Even…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
As is known that various dynamical systems including all Hamiltonian systems preserve volume in phase space. This qualitative geometrical property of the analytical solution should be respected in the sense of Geometric Integration. This…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
Acoustic waves in a slightly compressible fluid saturating porous periodic structure are studied using two complementary approaches: 1) the periodic homogenization (PH) method provides effective model equations for a general dynamic problem…
A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations are introduced, which is based on the principle of allowing quanta of mass to pass through faces of a Cartesian finite volume grid. The…
The compact Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. It is further developed to be more flexible in solving the…
Solving the electronic structure problem on a universal-gate quantum computer within the variational quantum eigensolver (VQE) methodology requires constraining the search procedure to a subspace defined by relevant physical symmetries.…
We introduce a framework for developing efficient and interpretable climate emulators (CEs) for economic models of climate change. The paper makes two main contributions. First, we propose a general framework for constructing carbon-cycle…
Classical simulation of molecular systems is limited by exponential scaling, a hurdle quantum algorithms like Variational Quantum Eigensolvers (VQEs) aim to overcome. Although ADAPT-VQE enhances VQEs by dynamically building ans\"atze, it…
The self-consistent modeling of vacuum polarization due to virtual electron-positron fluctuations is of relevance for many near term experiments associated with high intensity radiation sources and represents a milestone in describing…
We present two strategies to enhance the dynamical entanglement transfer from continuous variable (CV) to finite dimensional systems by employing multiple qubits. First, we consider the entanglement transfer to a composite finite…